A NOTE ON REDUCTIONS OF 2-DIMENSIONAL CRYSTALLINE GALOIS REPRESENTATIONS

Let p be an odd prime number, K-f the finite unramified extension of Q(p) of degree f and G(Kf) its absolute Galois group. We construct analytic families of etale (phi, Gamma(Kf))-modules which give rise to some families of 2-dimensional crystalline representations of G(Kf) with length of filtration >= p. As an application we prove that the modulo p reductions of the members of each such family (with respect to appropriately chosen Galois-stable lattices) are constant.